Question

a+b=a³+b³=1.Cm a²+b²=a⁴+b⁴

Answer 1

\(a+b=a^3+b^3=1\)

\(\Leftrightarrow a+b=\left(a+b\right)\left(a^2-ab+b^2\right)=1\)

\(\Leftrightarrow a^2-ab+b^2=1\)

\(\Leftrightarrow\left(a^2+2ab+b^2\right)-3ab=1\)

\(\Leftrightarrow\left(a+b\right)^2-3ab=1\)

\(\Leftrightarrow1-3ab=1\)

\(\Rightarrow ab=0\)

Ta có : \(\left(a+b\right)^2=1\)

\(\Leftrightarrow a^2+b^2+2ab=1\)

\(\Rightarrow a^2+b^2=1\) (1)

\(\Leftrightarrow\left(a^2+b^2\right)^2=a^4+b^4+2\left(ab\right)^2=1\)

\(\Rightarrow a^4+b^4=1\)(2)

Từ (1) ; (2) => đpcm

Answer 2

thank